# Speakers' Corner

Named after the renowned corner of Hyde Park in London, the Speakers' Corner seminars are a platform for everyone who would like to share their research. Do you have a new preprint and want to create an accompanying video lecture or just a cool result you would like to share with the community? Speakers' corner allows you to create, advertise and share your talk via Virtual Science Forum platform.

### Give a talk

The series is hence on a "self-invitation" basis, where you register for giving a talk through the Registration Form and bring your own audience. Every week, an announcement email is sent to the Speakers' Corner mailing list (register here) containing all of the upcoming talks. That way, more potential participants will learn about your talk and may decide to join.

## How it works

- Pick the topic of your talk, date and time (must be at least two weeks in the future), and make sure all your co-authors know about your presentation and agree.
- Fill in the Registration Form
- VSF:
- checks availability of your time slot and confirm the date
- creates the zoom meeting, opens the registration, and gives you the host key

- Advertising your talk:
- make sure to
**advertise your talk at your institution**and**invite participants to register for the talk** - tweet at @VirtualSciForum with the hashtag #VSFSpeakersCorner and we will retweet your talk info
- VSF announces your talk in the VSF Speakers' Corner mailing list and on this website

- make sure to
- Preparing for your talk:
- check that your screen resolution is set to lower than 1080p. This ensures the video captured by your camera while you speak will be not appear too small in the recording.

- You are welcome to moderate your talk yourself as well as invite a colleague to be your moderator
- VSF records your talk, forwards it to you for approval, and publishes it in the YouTube channel

## Upcoming talks

There are no upcoming talks at the moment, apply here to present one.

## Recordings

### Quantum weight

**By Yugo Onishi (Massachusetts Institute of Technology)**

**Authors:** Yugo Onishi, Liang Fu

**Preprint:** arXiv:2401.13847

We introduce the concept of quantum weight as a fundamental property of insulating states of matter that is encoded in the ground-state static structure and measures quantum fluctuation in electrons' center of mass. We find a sum rule that directly relates quantum weight -- a ground state property -- with the negative-first moment of the optical conductivity above the gap frequency. Building on this connection to optical absorption, we derive both an upper bound and a lower bound on quantum weight in terms of electron density, dielectric constant, and energy gap. Therefore, quantum weight constitutes a key material parameter that can be experimentally determined from X-ray scattering.

### Chiral adiabatic transmission protected by Fermi surface topology

**By Kostas Vilkelis (TU Delft)**

**Authors:** Isidora Araya Day, Kostas Vilkelis, Antonio L. R. Manesco, A. Mert Bozkurt, Valla Fatemi, Anton R. Akhmerov

**Preprint:** arXiv:2311.17160

We demonstrate that Andreev modes that propagate along a transparent Josephson junction have a perfect transmission at the point where three junctions meet. The chirality and the number of quantized transmission channels is determined by the topology of the Fermi surface and the vorticity of the superconducting phase differences at the trijunction. We explain this chiral adiabatic transmission (CAT) as a consequence of the adiabatic evolution of the scattering modes both in momentum and real space. We identify an effective energy barrier that guarantees quantized transmission. We expect that CAT is observable in nonlocal conductance and thermal transport measurements. Furthermore, because it does not rely on particle-hole symmetry, CAT is also possible to observe directly in metamaterials.

### Proof-of-work consensus by quantum sampling

**By Peter Rohde (BTQ & Macquarie University)**

**Authors:** Deepesh Singh, Boxiang Fu, Gopikrishnan Muraleedharan, Chen-Mou Cheng, Nicolas Roussy Newton, Peter P. Rohde, Gavin K. Brennen

**Preprint:** arXiv:2305.19865

Since its advent in 2011, boson-sampling has been a preferred candidate for demonstrating quantum advantage because of its simplicity and near-term requirements compared to other quantum algorithms. We propose to use a variant, called coarse-grained boson-sampling (CGBS), as a quantum Proof-of-Work (PoW) scheme for blockchain consensus. The users perform boson-sampling using input states that depend on the current block information, and commit their samples to the network. Afterward, CGBS strategies are determined which can be used to both validate samples and to reward successful miners. By combining rewards to miners committing honest samples together with penalties to miners committing dishonest samples, a Nash equilibrium is found that incentivizes honest nodes. The scheme works for both Fock state boson sampling and Gaussian boson sampling and provides dramatic speedup and energy savings relative to computation by classical hardware.

### Design of a Majorana trijunction

**By Juan Daniel Torres Luna (TU Delft)**

**Authors:** Juan Daniel Torres Luna, Sathish R. Kuppuswamy, Anton R. Akhmerov

**Preprint:** arXiv:2307.03299

Braiding of Majorana states demonstrates their non-Abelian exchange statistics. One implementation of braiding requires control of the pairwise couplings between all Majorana states in a trijunction device. In order to have adiabaticity, a trijunction device requires the desired pair coupling to be sufficently large and the undesired couplings to vanish. In this work, we design and simulate of a trijunction device in a two-dimensional electron gas with a focus on the normal region that connects three Majorana states. We use an optimisation approach to find the operational regime of the device in a multi-dimensional voltage space. Using the optimization results, we simulate a braiding experiment by adiabatically coupling different pairs of Majorana states without closing the topological gap. We then evaluate the feasibility of braiding in a trijunction device for different shapes and disorder strengths.

### Real-space multifold degeneracy in graphene irradiated by twisted light

**By Suman Aich (Indiana University Bloomington)**

**Authors:** Suman Aich, Babak Seradjeh

**Preprint:** arXiv:2311.04792

We report the theoretical discovery of real-space multifold degenerate Floquet-Bloch states in monolayer graphene coherently driven by twisted circulalry-polarized light. Using Floquet theory, we characterize the real-space structure of quasienergies and Floquet modes in terms of the orbital angular momentum and radial vortex profile of light. We obtain the effective real-space Floquet Hamiltonian and show it supports crossings of Floquet modes, especially at high-symmetry \(K\) and \(\Gamma\) points of graphene, at specific radial positions from the vortex center. At specific frequencies, the vortex bound states form a multifold degenerate structure in real-space. This structure is purely dynamically generated and controlled by the frequency and intensity of twisted light. We discuss the experimental feasibility of observing and employing the real-space multifold degeneracy for coherent optoelectronic quantum state engineering.

### Pymablock: A software package for constructing effective models

**By Isidora Araya Day (TU Delft)**

**Authors:** Isidora Araya Day, Sebastian Miles, Daniel Varjas, Anton Akhmerov

**Preprint:** arXiv:

In the study of quantum systems, effective models serve as a compact and insightful representation. They reduce the complex Hilbert space to a manageable low energy subspace, making the Hamiltonian interpretable and its observables computationally friendly. However, the construction of an effective Hamiltonian, which involves the application of perturbation theory, can be a daunting task, especially when dealing with large Hilbert spaces, high perturbative orders, or multiple perturbations.

In this talk, we introduce an algorithm designed to streamline this process. Our algorithm is capable of constructing both symbolic and numeric low energy models with computational efficiency. It is versatile, with applications ranging from superconducting circuits and tight-binding models to interacting Hamiltonians and more.

See our documentation at https://pymablock.readthedocs.io.

### Double-Fourier engineering of Josephson energy-phase relationships applied to diodes

**By A. Mert Bozkurt (TU Delft, Quantum Tinkerer)**

**Authors:** A. Mert Bozkurt, Jasper Brookman, Valla Fatemi, Anton R. Akhmerov

**Preprint:** arXiv:2307.04830

We present a systematic method to design arbitrary energy-phase relations using parallel arms of two series Josephson tunnel junctions each. Our approach employs Fourier engineering in the energy-phase relation of each arm and the position of the arms in real space. We demonstrate our method by engineering the energy-phase relation of a near-ideal superconducting diode, which we find to be robust against the imperfections in the design parameters. Finally, we show the versatility of our approach by designing various other energy-phase relations.

### Revival of Quadratic Dirac fermions and the competition of ordered states in twisted bilayer graphene

**By Julian Ingham (Columbia University)**

**Authors:** Julian Ingham, Tommy Li, Mathias Scheurer, Harley Scammell

**Preprint:** arXiv:2308.00748

Twisted bilayer graphene (TBG) exhibits an interesting phase diagram as a function of electron density — when the number of electrons per moir\'e unit cell \(\nu\) is an integer, insulating and nematic states are observed, with superconductivity appearing as \(\nu\) is increased past integer values. The fourfold degenerate bands near charge neutrality feature Dirac fermions, and experiments have observed an effect known as the “Dirac revival”: at integer values of \(\ nu\) the density ‘resets’ to the charge neutrality point, so the system is described by a Dirac theory even away from charge neutrality. In this talk I will describe a theoretical proposal in which these revived Dirac fermions have a small velocity, so that their dispersion is approximately quadratic in a range of energies. The quadratic Dirac fermions result in a logarithmic enhancement of interaction effects, which does not appear for a linear dispersion. The resulting non-trivial RG flow produces nematic and insulating states near integer fillings, which give way to superconducting states past a critical relative doping, and predicts phases which resolve several experimental puzzles — producing T-IVC insulating states for repulsive interactions, explaining the results of very recent STM experiments, alongside nodal \(A_2\) superconductivity near \(\nu=2\), whose properties can explain puzzles in tunnelling studies of the superconducting state. The model also explains why superconductivity is generally not observed when TBG is aligned with an hBN substrate, why superconductivity is less robust near \(\nu=0\) and 1 than \(\nu=2\), the asymmetry of the phase diagram between electron and hole doping, and the transition from a gapless to gapped charge neutrality point as a function of strain seen in STM — unifying many aspects of the phase diagram with a single theoretical model.

### Exact solution for the filling-induced thermalization transition in a 1D fracton system

**By Brian Skinner (Ohio State)**

**Authors:** Calvin Pozderac, Steven Speck, Xiaozhou Feng, David A. Huse, Brian Skinner

**Preprint:** arXiv:2210.02469

We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system exhibits a continuous phase transition between a weakly fragmented ("thermalizing") phase and a strongly fragmented ("nonthermalizing") phase as a function of the number density of particles. Here, by mapping to two different problems in combinatorics, we identify an exact solution for the critical density \(n_c\). Specifically, when evolution proceeds by operators that act on \(\ell\) contiguous sites, the critical density is given by \(n_c = 1/(\ell -2)\). We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent \(\nu = 2\). We confirm our theoretical results with numeric simulations. In the thermalizing phase the dynamical exponent is subdiffusive: \(z=4\), while at the critical point it increases to \(z_c \gtrsim 6\).

### Erroneous Statistics in Physical Review Physics Education Research

**By Michael B. Weissman (University of Illinois at Urbana-Champaign)**

**Authors:** M. B. Weissman

**Preprint:** arXiv:2101.05647

The American Physical Society publication Physical Review Physics Education Research focuses on questions that are essentially social science. Unfortunately, it routinely publishes and promotes papers that make egregious errors in statistical reasoning, particularly in causal inference. As a result policy recommendations based on PRPER papers can rest on causal conclusions that are unsupported by evidence and sometimes (e.g. on use of GREs) flatly contradicted by the evidence. I will describe just one typical erroneous paper to illustrate the technical issues, while providing references for critiques of many others. The PRPER editorial team has an express policy of resisting the type of error correction traditionally employed by Physical Review.

### Josephson-Current Signatures of Unpaired Floquet Majorana Bound States

**By Rekha Kumari (Indian Institute of Technology Kanpur, India)**

**Authors:** Rekha Kumari, Babak Seradjeh, Arijit Kundu

**Preprint:** arXiv:2301.07707

We theoretically study the transport signatures of unpaired Floquet Majorana bound states in the Josephson current of weakly linked, periodically driven topological superconductors. We obtain the occupation of the Floquet Majorana modes in the presence of weak coupling to thermal leads analytically, and show that, similar to static superconductors, the Josephson current involving Floquet Majorana bound states is also \(4\pi\)-periodic in the phase difference across the junction, and also depends linearly on the coupling between superconductors. Moreover, unlike the static case, the amplitude of the Josephson current can be tuned by setting the unbiased chemical potential of the driven superconductors at multiple harmonics of the drive frequency. As a result, we uncover a Josephson Floquet sum rule for driven superconductors. We confirm our analytical expressions for Josephson current, the occupation of Floquet bands, and a perturbative analysis of the quasienergies with numerically exact results.

### Interacting topological quantum chemistry of Mott atomic limits

**By Martina Ondina Soldini (University of Zurich)**

**Authors:** Martina O. Soldini, Nikita Astrakhantsev, Mikel Iraola, Apoorv Tiwari, Mark H. Fischer, Roser Valentí, Maia G. Vergniory, Glenn Wagner, Titus Neupert

**Preprint:** arXiv:2209.10556

Topological quantum chemistry (TQC) is a successful framework for identifying (non-interacting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at high symmetry momenta, which are attainable from first principles calculations, a band structure can either be classified as an atomic limit, in other words adiabatically connected to independent electronic orbitals on the respective crystal lattice, or it is topological. For interacting systems, there is no single-particle band structure and hence, the TQC machinery grinds to a halt. We develop a framework analogous to TQC, but employing n-particle Green's function to classify interacting systems. Fundamentally, we define a class of interacting reference states that generalize the notion of atomic limits, which we call Mott atomic limits. Our formalism allows to fully classify these reference states (with n=2), which can themselves represent symmetry protected topological states. With this, we establish Mott atomic limit states as a generalisation of the atomic limits to interacting systems.

### Driven Andreev molecule

**By Andriani Keliri (LPTHE, Sorbonne University)**

**Authors:** Andriani Keliri, Benoît Douçot

**Preprint:** arXiv:2208.11541

We study the three terminal S-QD-S-QD-S Josephson junction biased with commensurate voltages. In the absence of voltage bias, the Andreev bound states (ABS) on each quantum dot hybridize and form an Andreev molecule, producing non-local effects in the Josephson current. However, the range of the hybridization is limited by the superconducting coherence length \(\xi_0\).

Application of commensurate dc voltages makes the system time-periodic, and the equilibrium ABS evolve into ladders of resonances with a finite lifetime due to multiple Andreev reflection processes. We use Floquet theory to map to a tight-binding model, and we calculate the Floquet spectrum and the subgap current. When the distance between the dots is \(R\sim \xi_0,\) we find level splitting and modification of the subgap structure due to the proximity of the two junctions. Moreover, in the regime of large dot separation \(R\gg \xi_0,\) we find that the periodic driving induces long-range coupling between the dots.

### Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene

**By Aleksander Sanjuan Ciepielewski (MagTop, Institute of Physics, Polish Academy of Sciences)**

**Authors:** Aleksander Sanjuan Ciepielewski, Jakub Tworzydło, Timo Hyart, Alexander Lau

**Preprint:** arXiv:2208.08366

Magic-angle twisted bilayer graphene exhibits quasi-flat low-energy bands with Van Hove singularities close to the Fermi level. These singularities play an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. In this work, we study the correspondence of four-terminal conductance and the Fermi surface topology as a function of the twist angle, pressure, and energy in mesoscopic, ballistic samples of small-angle twisted bilayer graphene. We establish a correspondence between features in the wide-junction conductance and the presence of van Hove singularities in the density of states. Moreover, we identify additional transport features, such as a large, pressure-tunable minimal conductance, conductance peaks coinciding with non-singular band crossings, and unusually large conductance oscillations as a function of the system size. Our results suggest that twisted bilayer graphene close the magic angle is a unique system featuring simultaneously large conductance due to the quasi-flat bands, strong quantum nonlinearity due to the Van Hove singularities and high sensitivity to external parameters, which could be utilized in high-frequency device applications and sensitive detectors.

### Measurement-induced phase transitions on dynamical quantum trees

**By Xiaozhou Feng (The Ohio State University)**

**Authors:** Xiaozhou Feng, Brian Skinner, Adam Nahum

**Preprint:** arXiv:2210.07264

Monitored many-body systems fall broadly into two dynamical phases, "entangling" or "disentangling", separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with "real" measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of "real" measurements with the case of "forced" measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.

### Polaron spectroscopy of a bilayer excitonic insulator

**By Ivan Amelio (ETH Zurich)**

**Authors:** Ivan Amelio, Neil Drummond, Eugene Demler, Richard Schmidt, Atac Imamoglu

**Preprint:** arXiv:2210.03658

Recent advances in fabrication of two dimensional materials and their moiré heterostructures have opened up new avenues for realization of ground-state excitonic insulators, where the structure spontaneously develops a finite interlayer electronic polarization. We propose and analyze a scheme where an optically generated intralayer exciton is screened by excitations out of the excitonic insulator to form interlayer polarons. Using Quantum Monte-Carlo calculations we first determine the binding energy of the biexciton state composed of inter- and intralayer excitons, which plays a central role in understanding polaron formation. We describe the excitations out of the ground-state condensate using BCS theory and use a single interacting-quasiparticle-pair excitation Ansatz to describe dynamical screening of optical excitations. Our predictions carry the hallmarks of the excitonic insulator excitation spectrum and show how changing the interlayer exciton binding energy by increasing the layer separation modifies the optical spectra.

### Unprotected edge modes in quantum spin Hall insulator candidate materials

**By Wojciech Brzezicki (Jagiellonian University, Krakow)**

**Authors:** Nguyen Minh Nguyen, Giuseppe Cuono, Rajibul Islam, Carmine Autieri, Timo Hyart, Wojciech Brzezicki

**Preprint:** arXiv:2209.06912

The experiments in quantum spin Hall insulator candidate materials, such as HgTe/CdTe and InAs/GaSb heterostructures, indicate that in addition to the topologically protected helical edge modes these multilayer heterostructures may also support additional edge states, which can contribute to the scattering and the transport. We use first-principles calculations to derive an effective tight-binding model for HgTe/CdTe, HgS/CdTe and InAs/GaSb heterostructures, and we show that all these materials support additional edge states which are sensitive to the edge termination. We trace the microscopic origin of these states back to a minimal model supporting flat bands with a nontrivial quantum geometry that gives rise to polarization charges at the edges. We show that the polarization charges transform into the additional edge states when the flat bands are coupled to each other and to the other states to form the Hamiltonian describing the full heterostructure. Interestingly, in the HgTe/CdTe quantum wells the additional edge states are far away from the Fermi level so that they do not contribute to the transport but in the HgS/CdTe and InAs/GaSb heterostructures they appear within the bulk energy gap giving rise to the possibility of multimode edge transport. Finally, we demonstrate that because these additional edge modes are non-topological it is possible to remove them from the bulk energy gap by modifying the edge potential for example with the help of a side gate or chemical doping.

### Spatial separation of spin currents in transition metal dichalcogenides

**By Antonio Manesco (Delft University of Technology)**

**Authors:** Antonio L. R. Manesco, Artem Pulkin

**Preprint:** arXiv:2206.07333

We theoretically predict spatial separation of spin-polarized ballistic currents in transition metal dichalcogenides (TMDs) due to trigonal warping. We quantify the effect in terms of spin polarization of charge carrier currents in a prototypical 3-terminal ballistic device where spin-up and spin-down charge carriers exit different leads. We show that the magnitude of the current spin polarization depends strongly on the charge carrier energy and the direction with respect to crystallographic orientations in the device. We study the (negative) effect of lattice imperfections and disorder on the observed spin polarization. Our investigation provides an avenue towards observing spin discrimination in a defect-free time reversal-invariant material.

### Pfaffian invariant identifies magnetic obstructed atomic insulators

**By Isidora Araya Day (QuTech, TU Delft)**

**Authors:** Isidora Araya Day, Anastasiia Varentcova, Daniel Varjas, Anton R. Akhmerov

**Preprint:** arXiv:2209.00029

We derive a \(\mathbb{Z}_4\) topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a \(C_4 \mathcal{T}\) symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four \(C_4 \mathcal{T}\)-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a \(C_4 \mathcal{T}\)-symmetric model that interpolates between them. The phase diagram shows that \(C_4 \mathcal{T}\) insulators allow \(\pm 1\) and \(2\) changes of the invariant, where the latter is overlooked by symmetry indicators.

### What is the relation between activation energy and band gap in a 2D insulator?

**By Yi Huang (University of Minnesota)**

**Authors:** Yi Huang, Brian Skinner, Boris Shklovskii

**Preprint:** arXiv:2201.11652

What can one actually tell about the band gap from the activation energy for conductivity in a 2D material? At first glance, it seems like the activation energy should be equal to half the band gap if the Fermi level is in the middle of the gap. But this simple relation is often strongly violated in experiments, where it is common to observe a much smaller activation energy. In this talk, we will review some examples of relevant experiments in topological insulators, bilayer graphene, and Mott insulators in twisted moiré bilayers. We will show theoretically how disorder, even when present at a very low level, almost inevitably lowers the activation energy to a nonuniversal value that is parametrically smaller than the band gap. We will further show how a sufficiently large disorder can produce an apparent insulator-to-metal transition.

### Greedy optimization of the geometry of Majorana Josephson junctions

**By André Melo (Kavli Institute of Nanoscience, Delft University of Technology)**

**Authors:** André Melo, Tanko Tanev, Anton R. Akhmerov

**Preprint:** arXiv:2205.05689

Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the topological gap, the question of how to construct optimal geometries remains unexplored. We introduce a greedy numerical algorithm to optimize the shape of Majorana junctions. The core of the algorithm relies on perturbation theory and is embarrassingly parallel, which allows it to explore the design space efficiently. By introducing stochastic variations in the junction Hamiltonian, we avoid overfitting geometries to specific system parameters. Furthermore, we constrain the optimizer to produce smooth geometries by applying image filtering and fabrication resolution constraints. We run the algorithm in various setups and find that it reliably produces geometries with increased topological gaps over large parameter ranges. The results are robust to variations in the optimization starting point and the presence of disorder, which suggests the optimizer is capable of finding global maxima.

### The Josephson diode effect in supercurrent interferometers

**By Rubén Seoane Souto (Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark Division of Solid State Physics and NanoLund, Lund University, S-22100 Lund, Sweden)**

**Authors:** Rubén Seoane Souto, Martin Leijnse, and Constantin Schrade

**Preprint:** arXiv:2205.04469

A Josephson diode is a non-reciprocal circuit element that supports a larger dissipationless super-current in one direction than in the other. In this work, we propose and theoretically study a class of Josephson diodes based on supercurrent interferometers containing mesoscopic Josephson junctions, such as point contacts or quantum dots, which are not diodes themselves but possess non-sinusoidal current-phase relations. We show that such Josephson diodes have several important advantages, like being electrically tunable and requiring neither Zeeman splitting nor spin-orbit coupling, only time-reversal breaking by a magnetic flux. We also show that our diodes have a characteristic AC response, revealed by the Shapiro steps. Even the simplest realization of our Josephson diode paradigm that relies on only two junctions can achieve efficiencies of up to ∼ 40% and far greater efficiencies are achievable by concatenating multiple interferometer loops.

### Theory of the supercurrent diode effect in Rashba superconductors with arbitrary disorder

**By Stefan Ilić (Centro de Fisica de Materiales (CFM-MPC), San Sebastian, Spain)**

**Authors:** Stefan Ilić, Sebastian Bergeret

**Preprint:** arXiv:2108.00209

We calculate the non-reciprocal critical current and quantify the supercurrent diode effect in Rashba superconductors with arbitrary disorder, using the quasiclassical Eilenberger equation. The non-reciprocity is caused by the helical superconducting state, which appears when both inversion and time-reversal symmetries are broken. In the absence of disorder, we find a very strong diode effect, with the non-reciprocity exceeding 40% at optimal temperatures, magnetic fields and spin-orbit coupling. We establish that the effect persists even in the presence of strong disorder. We show that the sign of the diode effect changes as magnetic field and disorder are increased, reflecting the changes in the nature of the helical state.

### Automated reconstruction of bound states in bilayer graphene quantum dots

**By Jozef Bucko (Institute for Computational Science, University of Zurich)**

**Authors:** Jozef Bucko, Frank Schäfer, František Herman, Rebekka Garreis, Chuyao Tong, Annika Kurzmann, Thomas Ihn, Eliska Greplova

**Preprint:** arXiv:2203.00697

Bilayer graphene is a nanomaterial that allows for well-defined, separated quantum states to be defined by electrostatic gating and, therefore, provides an attractive platform to construct tunable quantum dots. When a magnetic field perpendicular to the graphene layers is applied, the graphene valley degeneracy is lifted, and splitting of the energy levels of the dot is observed. Given the experimental ability to engineer this energy valley splitting, bilayer graphene quantum dots have a great potential for hosting robust qubits. Although bilayer graphene quantum dots have been recently realized in experiments, it is critically important to devise robust methods that can identify the observed quantum states from accessible measurement data. Here, we develop an efficient algorithm for extracting the model parameters needed to characterize the states of a bilayer graphene quantum dot completely. We introduce a Hamiltonian-guided random search method and demonstrate robust identification of quantum states on both simulated and experimental data.

### Superconducting diode effect in InSb nanowires Josephson junctions

**By Bomin Zhang (University of Pittsburgh)**

**Authors:** Bomin Zhang, Zhuang Li, Victor Aguilar, Po Zhang, Mihir Pendharkar, Connor Dempsey, Joon Sue Lue, Sean Harrington, Ghada Badawy, Sasa Gazibegovic, Jason Jung, An-Hsi Chen, Susheng Tan, Marcel Verheijen, Moira Hocevar, Erik Bakkers, Chris Palmstrøm, Sergey Frolov

**Preprint:** arXiv:Not submitted yet

We study Josephson Junction in InSb nanowires with 15nm Tin shells. We observe critical current diffraction patterns skewed and inversion-symmetric in the magnetic field and bias direction. The effect is stronger when the external magnetic field is aligned perpendicular to the nanowire, in the substrate plane. i.e. in the most likely direction of the effective spin-orbit field in the junction. The effect is also tunable by the gate voltage. We discuss this effect in the context of phi0-Josephson junction physics, one consequence of which is known in recent literature as the superconducting diode effect. We consider alternative explanations such as the effective magnetic field and perform numerical simulations to understand our findings.

### Can Caroli-de Gennes-Matricon and Majorana vortex states be distinguished in the presence of impurities?

**By Bruna Mendonca (University of Sao Paulo)**

**Authors:** Bruna S. de Mendonça, Antonio L. R. Manesco, Nancy Sandler, Luis G. G. V. Dias da Silva

**Preprint:** arXiv:2204.05078

Majorana zero modes states (MZMs) are predicted to appear as bound states in vortices of topological superconductors. MZMs are pinned at zero energy and have zero charge due to particle-hole symmetry. MZMs in vortices of topological superconductors tend to coexist with other subgap states, named Caroli-de Gennes-Matricon (CdGM) states. The distinction between MZMs and CdGM is limited since current experiments rely on zero-bias peak measurements obtained via scanning tunneling spectroscopy. In this work, we show that a local impurity potential can push CdGM states to zero energy. Furthermore, the finite charge in CdGM states can also drop to zero under the same mechanism. We establish, through exploration of the impurity parameter space, that these two phenomena generally happen in consonance. This means that energy and charge shifts in CdGM may be enough to imitate spectroscopic signatures of MZMs.

### Topological defects in a double-mirror quadrupole insulator displace diverging charge

**By Isidora Araya Day (QuTech and Kavli Institute of Nanoscience, TU Delft)**

**Authors:** Isidora Araya Day, Anton R. Akhmerov, Daniel Varjas

**Preprint:** arXiv:2202.07675

We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a parametric defect and a disclination. Against the expectations, we find that the local charge density decays as \(\sim 1/r^2\) with distance, leading to a diverging defect charge. We identify sublattice symmetry and not higher order topology as the origin of the previously reported charge quantization.

### Selective Control of Conductance Modes in Multi-terminal Josephson Junctions

**By Mohit Gupta (University of Minnesota)**

**Authors:** Gino V. Graziano, Mohit Gupta, Mihir Pendharkar, Jason T. Dong, Connor P. Dempsey, Chris Palmstrøm, Vlad S. Pribiag

**Preprint:** arXiv:2201.01373

The Andreev bound state spectra of multi-terminal Josephson junctions form an artificial band structure, which is predicted to host tunable topological phases under certain conditions. However, the number of conductance modes between the terminals of multi-terminal Josephson junction must be few in order for this spectrum to be experimentally accessible. In this work we employ a quantum point contact geometry in three-terminal Josephson devices. We demonstrate independent control of conductance modes between each pair of terminals and access to the single-mode regime coexistent with the presence of superconducting coupling. These results establish a full platform on which to realize tunable Andreev bound state spectra in multi-terminal Josephson junctions.

### SU(2) hadrons on a quantum computer

**By Jinglei Zhang (Instute for Quantum Computing / University of Waterloo)**

**Authors:** Yasar Atas, Jinglei Zhang, Randy Lewis, Amin Jahanpour, Jan F. Haase, Christine A. Muschik

**Preprint:** arXiv:2102.08920

We realize, for the first time, a non-Abelian gauge theory with both gauge and matter fields on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Quantum computers are able to create important new opportunities for ongoing essential research on gauge theories by providing simulations that are unattainable on classical computers. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a resource-efficient approach that not only allows the implementation of a full SU(2) gauge theory on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.

### Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures

**By Nisarga Paul (Massachusetts Institute of Technology)**

**Authors:** Nisarga Paul, Yang Zhang, Liang Fu

**Preprint:** arXiv:2111.01805

Van der Waals (vdW) heterostructures formed by two-dimensional magnets and semiconductors have provided a fertile ground for fundamental science and for spintronics. In this talk I discuss two main results: (1) a first-principles calculations finding a proximity exchange splitting of 14 meV equivalent to an effective Zeeman field of 120 T in the vdW magnet-semiconductor heterostructure MoS2/CrBr3 and (2) the appearance of a flat Chern band in the electronic bandstructure of 2D magnet - semiconductor heterostructures when the magnetic layer hosts chiral spin textures such as skyrmions. The latter result is derived in a completely general continuum model. More specifically, a flat Chern band is found at a "magic" value of magnetization (~0.2) for Schrödinger electrons, and it generally occurs for Dirac electrons. I also discuss possible connections to skyrmions in magnetic TIs and spintronics.

### Longitudinal resistance oscillations in InSbAs 2DEGs in a Quantum Hall regime

**By Ivan Kulesh (QuTech, Delft University of Technology)**

**Authors:** Ivan Kulesh, Mark van Blankenstein, Candice Thomas, Di Xiao, Geoffrey C. Gardner, Michael J. Manfra, Srijit Goswami

**Preprint:** arXiv:

Integer quantum Hall states interacting with a superconducting electrode, are predicted to form Andreev edge states. This effect is expected to exhibit an oscillatory interference pattern in the longitudinal resistance, measured with respect to the grounded superconducting lead. In InSb-based two-dimensional electron gases we observe pronounced longitudinal resistance oscillations. However, we verify that the origin of such oscillation is not related to the superconductivity, but rather, transport through the bulk in the disordered quantum Hall regime. Understanding the origin and location in parameter states of these oscillations is important to clearly distinguish between trivial and superconducting effects in the quantum Hall regime.

### Quantum anomalous Hall effect from inverted charge transfer gap: application to moire transition metal dichalcogenide bilayers

**By Trithep Devakul (MIT)**

**Authors:** Trithep Devakul, Liang Fu

**Preprint:** arXiv:2109.13909

A general mechanism is presented by which topological physics arises in strongly correlated systems without flat bands. Starting from a charge transfer insulator, topology emerges when the charge transfer energy between the cation and anion is reduced to invert the lower Hubbard band and the spin-degenerate charge transfer band. A universal low-energy theory is developed for the inversion of charge transfer gap in an \(xy\) antiferromagnet. The inverted state is found to be a quantum anomalous Hall (QAH) insulator with non-coplanar magnetism. Interactions play two essential roles in this mechanism: producing the Mott gap and quasiparticle bands necessary for band inversion, and driving non-coplanar magnetism after inversion. Our theory applies to and explains the recently observed QAH state in AB-stacked TMD bilayer MoTe\(_2\)/WSe\(_2\).

### Quantized Nonlinear Response in Ballistic Metals

**By Charles Kane (University of Pennsylvania)**

**Authors:** Charles Kane

**Preprint:** arXiv:2108.05870

A dramatic consequence of the role of topology in the structure of quantum matter is the existence of topological invariants that are reflected in quantized response functions. In this talk we will discuss a new variant on this theme. We introduce a non-linear frequency dependent D+1 terminal conductance that characterizes a D dimensional Fermi gas, generalizing the Landauer conductance in 1 dimension. For a 2D ballistic conductor we show that this conductance is quantized and probes the Euler characteristic of the Fermi sea. We critically address the roles of electrical contacts and of Fermi liquid interactions, and we propose experiments on 2D Dirac materials such as graphene using a triple point contact geometry.

### Ising superconductivity in few-layer stanene

**By Ding Zhang (Tsinghua University)**

**Authors:** Joseph Falson, Yong Xu, Menghan Liao, Yunyi Zang, Kejing Zhu, Chong Wang, Zetao Zhang, Hongchao Liu, Wenhui Duan, Ke He, Haiwen Liu, Jurgen H. Smet, Ding Zhang, Qi-Kun Xue

**Preprint:** arXiv:1903.07627

The two-dimensional crystalline superconductors possess a variety of exotic properties. For instance, their Cooper pairs can sustain a large in-plane magnetic field owning to the spin-orbital locking [1]. Here we report two-dimensional superconductivity in few layer stanene—ultrathin gray tin (111)—with an enhanced in-plane upper critical field. The emergence of superconductivity in stanene is unexpected because bulk gray tin is non-superconductive. We found superconductivity in few-layer stanene on PbTe/Bi2Te3/Si(111) substrate grown by molecular beam epitaxy [2]. The superconducting properties can be modulated by varying the substrate thickness. The band structure of this system is consistent with first-principles calculations, suggesting topologically non-trivial properties. Furthermore, few-layer stanene hosts enhanced in-plane upper critical fields that greatly exceed the conventional limit. Few-layer stanene is centrosymmetric and its electronic bands center around the Γ point. Therefore, the established Ising superconductivity for transition metal dichalcogenide does not apply. Instead, we propose a novel type of spin locking mechanism—dubbed type-II Ising pairing, which accounts for the large in-plane upper critical magnetic field in centrosymmetric superconductor with multiple degenerate orbitals [3].

- D. Zhang and J. Falson,
*Nanotechnology***32**, 502003 (2021). - M. Liao#, Y. Zang#, et al.
*Nat. Phys.***14**, 344-348 (2018). - J. Falson, et al.
*Science***367**, 1454 (2020).

### Mechanisms of Andreev reflection in quantum Hall graphene

**By Antonio Manesco (TU Delft)**

**Authors:** Antonio L. R. Manesco, Ian Matthias Flór, Chun-Xiao Liu, Anton R. Akhmerov

**Preprint:** arXiv:2103.06722

We simulate a hybrid superconductor-graphene device in the quantum Hall regime to identify the origin of downstream resistance oscillations in a recent experiment [Zhao et. al. Nature Physics 16, (2020)]. In addition to the previously studied Mach-Zehnder interference between the valley-polarized edge states, we consider disorder-induced scattering, and the previously overlooked appearance of the counter-propagating states generated by the interface density mismatch. Comparing our results with the experiment, we conclude that the observed oscillations are induced by the interfacial disorder, and that lattice-matched superconductors are necessary to observe the alternative ballistic effects.

### Topologically Localized Insulators

**By Bastien Lapierre (University of Zurich)**

**Authors:** Bastien Lapierre, Titus Neupert, Luka Trifunovic

**Preprint:** arXiv:2110.14651

In this talk I will show that fully localized, three-dimensional, time-reversal-symmetry-broken Anderson insulators support topologically distinct phases that can be labelled by integers. Any two such topologically localized phases are separated by a metallic phase. These novel topological phases are fundamentally distinct from insulators without disorder: they are guaranteed to host delocalized states along their insulating boundaries, giving rise to the quantized boundary Hall conductance whose value is determined by the integer invariant assigned to the bulk.

### SciPost and the reform of scientific publishing

**By Jean-Sébastien Caux (University of Amsterdam)**

**Authors:** Jean-Sébastien Caux

**Preprint:** arXiv:

SciPost is a not-for-profit publishing initiative conceived, implemented

and run by professional scientists. Leveraging the idea of openness, it aims to increase the utility and meaningfulness of the peer refereeing process. Committed to scientific quality, it aims to offer high-quality publishing venues, thereby bringing control of publishing into the hands of active academics.

SciPost also implements a cost-slashing, institutions-backed consortial

business model deprecating subscription fees or article processing charges, and aiming to shield scientists from the pernicious influence of profit-making in the publishing industry.

This talk will summarize operations since the launch of the portal in 2016, share experiences gained, and provide perspectives for future developments in the reform of scientific publishing.

### Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene

**By Yantao Li (Indiana University)**

**Authors:** Yantao Li, Adam Eaton, H. A. Fertig, Babak Seradjeh

**Preprint:** arXiv:2107.10687

We uncover a new type of magic-angle phenomena when an AA-stacked graphene bilayer is twisted relative to another graphene system with band touching. In the simplest case this constitutes a trilayer system formed by an AA-stacked bilayer twisted relative to a single layer of graphene. We find multiple anisotropic Dirac cones coexisting in such twisted multilayer structures at certain angles, which we call "Dirac magic." We trace the origin of Dirac magic angles to the geometric structure of the twisted AA-bilayer Dirac cones relative to the other band-touching spectrum in the moir\'e reciprocal lattice. The anisotropy of the Dirac cones and a concomitant cascade of saddle points induce a series of topological Lifshitz transitions that can be tuned by the twist angle and perpendicular electric field. We discuss the possibility of direct observation of Dirac magic as well as its consequences for the correlated states of electrons in this moir\'e system.

### Mysteries near the zero-field Wigner crystal transition in a 2D electron system

**By Brian Skinner (Ohio State University)**

**Authors:** Joseph Falson, Inti Sodemann, Brian Skinner, Daniela Tabrea, Yusuke Kozuka, Atsushi Tsukazaki, Masashi Kawasaki, Klaus von Klitzing, Jurgen H Smet

**Preprint:** arXiv:2103.16586

I will discuss recent experimental results on the low-temperature transport in a strongly interacting zinc-oxide-based high mobility two dimensional electron system. The data shows clear hallmarks of the long-anticipated transition between a Fermi liquid phase and a Wigner crystal phase at zero magnetic field. Other features of the data, however, suggest new mysteries in the vicinity of this transition. This talk will highlight those mysteries, and overview a number of sharp and unexpected questions that are implied by the data. I will focus on the resistivity at ultra-low temperatures as a function of electron concentration and spin polarization.

### Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayer MoTe2/WSe2

**By Yang Zhang (Massachusetts Institute of Technology)**

**Authors:** Yang Zhang, Trithep Devakul, Liang Fu

**Preprint:** arXiv:2107.02167

While transition metal dichalcogenide (TMD) based moire materials have been shown to host various correlated electronic phenomena, topological states have not been experimentally observed until now. In this work, using first principles calculations and continuum modeling, we reveal the displacement field induced topological moire bands in AB-stacked TMD heterobilayer MoTe2/WSe2. Valley contrasting Chern bands with non-trivial spin texture are formed from interlayer hybridization between MoTe2 and WSe2 bands of nominally opposite spins. Our study establishes a recipe for creating topological bands in AB stacked TMD bilayers in general, which provides a highly tunable platform for realizing quantum spin Hall and interaction induced quantum anomalous Hall effects.

### Cavity magnon-polaritons in cuprate parent compounds

**By Jonathan Curtis (Harvard University)**

**Authors:** Jonathan B. Curtis, Andrey Grankin, Nicholas R. Poniatowski, Victor M. Galitski, Prineha Narang, Eugene Demler

**Preprint:** arXiv:2106.07828

Cavity control of quantum matter may offer new ways to study and manipulate many-body systems. A particularly appealing idea is to use cavities to enhance superconductivity, especially in unconventional or high-\(T_c\) systems. Motivated by this, we propose a scheme for coupling Terahertz resonators to the antiferromagnetic fluctuations in a cuprate parent compound, which are believed to provide the glue for Cooper pairs in the superconducting phase. First, we derive the interaction between magnon excitations of the Ne\'el-order and polar phonons associated with the planar oxygens. This mode also couples to the cavity electric field, and in the presence of spin-orbit interactions mediates a linear coupling between the cavity and magnons, forming hybridized magnon-polaritons. This hybridization vanishes linearly with photon momentum, implying the need for near-field optical methods, which we analyze within a simple model. We then derive a higher-order coupling between the cavity and magnons which is only present in bilayer systems, but does not rely on spin-orbit coupling. This interaction is found to be large, but only couples to the bimagnon operator. As a result we find a strong, but heavily damped, bimagnon-cavity interaction which produces highly asymmetric cavity line-shapes in the strong-coupling regime. To conclude, we outline several interesting extensions of our theory, including applications to carrier-doped cuprates and other strongly-correlated systems with Terahertz-scale magnetic excitations.

### Supercurrent diode effect and finite momentum superconductivity

**By Noah F. Q. Yuan (Shenzhen JL Computational Science and Applied Research Institute)**

**Authors:** Noah F. Q. Yuan, Liang Fu

**Preprint:** arXiv:2106.01909

When both inversion and time-reversal symmetries are broken, the critical current of a superconductor can be nonreciprocal. In this work we show that in certain classes of two-dimensional superconductors with antisymmetric spin-orbit coupling, Cooper pairs acquire a finite momentum upon the application of an in-plane magnetic field, and as a result, critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal. This supercurrent diode effect is also manifested in the polarity-dependence of in-plane critical fields induced by a supercurrent. These nonreciprocal effects may be found in polar SrTiO\(_3\) film, few-layer MoTe\(_2\) in the \(T_d\) phase, and twisted bilayer graphene in which the valley degrees of freedom plays the role analogous to spin.

### Superconductivity provides a giant enhancement to the spin battery effect

**By Risto Ojajärvi (University of Jyväskylä)**

**Authors:** Risto Ojajärvi, Tero T. Heikkilä, P. Virtanen, M. A. Silaev

**Preprint:** arXiv:2103.07412

We develop a theory of the spin battery effect in superconductor/ferromagnetic insulator (SC/FI) systems taking into account the magnetic proximity effect. We demonstrate that the spin-energy mixing enabled by the superconductivity leads to the enhancement of spin accumulation by several orders of magnitude relative to the normal state. This finding can explain the recently observed giant inverse spin Hall effect generated by thermal magnons in the SC/FI system. We suggest a non-local electrical detection scheme which can directly probe the spin accumulation driven by the magnetization dynamics. We predict a giant Seebeck effect converting the magnon temperature bias into the non-local voltage signal. We also show how this can be used to enhance the sensitivity of magnon detection even up to the single-magnon level.

### Correlations and computational quantum transport: an approach for the automatic calculation of Feynman diagrams at large orders

**By Xavier Waintal (PHELIQS, CEA Grenoble, France)**

**Authors:** Marjan Maček, Philipp T. Dumitrescu, Corentin Bertrand, Bill Triggs, Olivier Parcollet, Xavier Waintal

**Preprint:** arXiv:2002.12372

Even in the simplest quantum nanoelectronic devices, such as quantum dots (Kondo effect, Coulomb blockade) or quantum point contacts (0.7 anomaly), electronic correlations play a central role. Yet, except in some specific situations, these correlations are beyond the reach of existing numerical techniques. In this talk, I will present our efforts to build algorithms that systematically and automatically calculate all Feynman diagrams up to very large order (10-22). As a first real life application, I will show how the technique can be used to solve the Kondo problem out-of-equilibrium.

### Correlation-induced valley topology in buckled graphene superlattices

**By Antonio Manesco (University of São Paulo)**

**Authors:** Antonio L. R. Manesco, Jose L. Lado

**Preprint:** arXiv:2104.00573

Flat bands emerging in buckled monolayer graphene superlattices have been recently shown to realize correlated states analogous to those observed in twisted graphene multilayers. Here, we demonstrate the emergence of valley topology driven by competing electronic correlations in buckled graphene superlattices. We show, both by means of atomistic models and a low-energy description, that the existence of long-range electronic correlations leads to a competition between antiferromagnetic and charge density wave instabilities, that can be controlled by means of screening engineering. Interestingly, we find that the emergent charge density wave has a topologically non-trivial electronic structure, leading to a coexistent quantum valley Hall insulating state. In a similar fashion, the antiferromagnetic phase realizes a spin-polarized quantum valley-Hall insulating state. Our results put forward buckled graphene superlattices as a new platform to realize interaction-induced topological matter.

### Multiplet supercurrent in Josephson tunneling circuits

**By André Melo (Kavli Institute of Nanoscience, Delft University of Technology)**

**Authors:** André Melo, Valla Fatemi, Anton R. Akhmerov

**Preprint:** arXiv:2104.11239

The multi-terminal Josephson effect allows DC supercurrent to flow at finite commensurate voltages. Existing proposals to realize this effect rely on nonlocal Andreev processes in superconductor-normal-superconductor junctions. However, this approach requires precise control over microscopic states and is obscured by dissipative current. We show that standard tunnel Josephson circuits also support multiplet supercurrent mediated only by local tunneling processes. Furtheremore, we observe that the supercurrents persist even in the high charging energy regime in which only sequential Cooper transfers are allowed. Finally, we demonstrate that the multiplet supercurrent in these circuits has a quantum geometric component that is distinguinshable from the well-known adiabatic contribution.

### Realization of the field-free Josephson diode

**By Mazhar Ali (Max Planck Institute for Microstructure Physics)**

**Authors:** Heng Wu, Yaojia Wang, Pranava K. Sivakumar, Chris Pasco, Stuart S. P. Parkin, Yu-Jia Zeng, Tyrel McQueen, Mazhar N. Ali

**Preprint:** arXiv:2103.15809

The superconducting analog to the semiconducting diode, the Josephson diode, has long been sought, with multiple avenues to realization proposed by theorists. Exhibiting magnetic-field free, single directional superconductivity with Josephson coupling of the supercurrent across a tunnel barrier, it would serve as the building-block for next-generation superconducting circuit technology. Here we realized the field-free Josephson diode using an inversion symmetry breaking heterostructure of \(\mathrm{NbSe_2/Nb_3Br_8/NbSe_2}\). We demonstrate, for the first time without magnetic field, the junction can be superconducting in one direction while normal in the opposite direction. Based on that, half-wave rectification of a square-wave excitation was achieved with low switching current density (\(~2.2\times 10^2 \mathrm{A/cm^2}\)), high rectification ratio (\(~10^4\)) and high robustness (at least \(10^4\) cycles). We also demonstrate symmetric \(\Delta I_\mathrm{c}\) (the difference between positive and negative critical currents) behavior with field and the expected Fraunhofer current phase relation of a Josephson junction. This realization raises fundamental questions about the Josephson effect through an insulator when breaking symmetry, and opens the door to ultralow power, high speed, superconducting circuits for logic and signal modulation.

### Quantum many-body topology of quasicrystals

**By Dominic Else (MIT)**

**Authors:** Dominic V. Else, Sheng-Jie Huang, Abhinav Prem, Andrey Gromov

**Preprint:** arXiv:2103.13393

In this paper, we characterize quasicrystalline interacting topological phases of matter i.e., phases protected by some quasicrystalline structure. We show that the elasticity theory of quasicrystals, which accounts for both "phonon" and "phason" modes, admits non-trivial quantized topological terms with far richer structure than their crystalline counterparts. We show that these terms correspond to distinct phases of matter and also uncover intrinsically quasicrystalline phases, which have no crystalline analogues. For quasicrystals with internal \(\mathrm{U}(1)\) symmetry, we discuss a number of interpretations and physical implications of the topological terms, including constraints on the mobility of dislocations in \(d=2\) quasicrystals and a quasicrystalline generalization of the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem. We then extend these ideas much further and address the complete classification of quasicrystalline topological phases, including systems with point-group symmetry as well as non-invertible phases. We hence obtain the "Quasicrystalline Equivalence Principle," which generalizes the classification of crystalline topological phases to the quasicrystalline setting.

### Superconductivity mediated by a third-electron: Spin-triplet superconductivity from excitonic eﬀect in doped band insulators

**By Valentin Crépel (MIT)**

**Authors:** Valentin Crépel and Liang Fu

**Preprint:** arXiv:arXiv:2012.08528 and arXiv:2103.12060

In this talk, I will comprehensively review the general electronic mechanism for superconductivity introduced in arXiv:2012.08528 and arXiv:2103.12060. There, it is shown that a non-retarded pairing interaction can be produced from the electron-electron repulsion itself through virtual inter-band transitions. The theory presented is analytically controlled by a strong-coupling expansion in the kinetic energy term and explicitly demonstrated in doped band insulators with the example of an extended Hubbard model. This work demonstrates a powerful method for studying strong coupling superconductivity. It also offers realistic new routes to realize unconventional superconducting state with, for instance, finite angular momentum or spin-triplet pairing.

### Flat band induced non-Fermi liquid behavior of multicomponent fermions

**By Pramod Kumar (Aalto University)**

**Authors:** Pramod Kumar, Sebastiano Peotta, Yosuke Takasu, Yoshiro Takahashi, Päivi Törmä

**Preprint:** arXiv:2005.05457

We investigate multicomponent fermions in a flat band and predict experimental signatures of non-Fermi liquid behavior. We use dynamical mean-field theory to obtain the density, double occupancy and entropy in a Lieb lattice for \(\mathcal{N} = 2\) and \(\mathcal{N} = 4\) components. We derive a mean-field scaling relation between the results for different values of \(\mathcal{N}\), and study its breakdown due to beyond-mean field effects. The predicted signatures occur at temperatures above the N\'eel temperature and persist in presence of a harmonic trapping potential, thus they are observable with current ultracold gas experiments.

### Deconfinement of Majorana vortex modes produces a superconducting Landau level

**By Michał Pacholski (Instituut-Lorentz, Universiteit Leiden)**

**Authors:** M. J. Pacholski, G. Lemut, O. Ovdat, İ. Adagideli, C. W. J. Beenakker

**Preprint:** arXiv:2101.08252

A spatially oscillating pair potential \(\Delta(r)=\Delta_0 e^{i K\cdot x}\) with momentum \(K>\Delta_0/\hbar v\) drives a deconfinement transition of the Majorana bound states in the vortex cores of a Fu-Kane heterostructure (a 3D topological insulator with Fermi velocity \(v\), on a superconducting substrate with gap \(\Delta_0\), in a perpendicular magnetic field). In the deconfined phase at zero chemical potential the Majorana fermions form a dispersionless Landau level, protected by chiral symmetry against broadening due to vortex scattering. The coherent superposition of electrons and holes in the Majorana Landau level is detectable as a local density of states oscillation with wave vector \(\sqrt{K^2-(\Delta_0/\hbar v)^2}\). The striped pattern also provides a means to measure the chirality of the Majorana fermions.

### Numerical evidence for marginal scaling at the integer quantum Hall transition

**By Elizabeth Dresselhaus (University of California, Berkeley)**

**Authors:** E. J. Dresselhaus, B. Sbierski, I. A. Gruzberg

**Preprint:** arXiv:2101.01716

The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling flow close to the critical fixed point in the parameter plane spanned by the longitudinal and Hall conductivities has been studied vigorously both by experiments and with numerical simulations. Despite all efforts, it is notoriously difficult to pin down the precise values of critical exponents, which seem to vary with model details and thus challenge the principle of universality. Recently, M. Zirnbauer [Nucl. Phys. B 941, 458 (2019)] has conjectured a conformal field theory for the transition, in which linear terms in the beta-functions vanish, leading to a very slow flow in the fixed point's vicinity which we term marginal scaling. In this work, we provide numerical evidence for such a scenario by using extensive simulations of various network models of the IQHT at unprecedented length scales. At criticality, we confirm the marginal scaling of the longitudinal conductivity towards the conjectured fixed-point value \(\sigma_{xx} = 2/\pi\). Away from criticality we describe a mechanism that could account for the emergence of an effective critical exponents \(\nu_{eff}\), which is necessarily dependent on the parameters of the model. We confirm this idea by exact numerical determination of \(\nu_{eff}\) in suitably chosen models.

### Amorphous topological phases protected by continuous rotation symmetry

**By Helene Spring (TU Delft)**

**Authors:** Helene Spring, Anton R. Akhmerov, Daniel Varjas

**Preprint:** arXiv:2012.12909

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. While the local disorder caused by the amorphous structure weakens the topological protection, we demonstrate that the edge remains protected from localization. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.

### Bloch-Lorentz magnetoresistance oscillations in delafossites

**By Kostas Vilkelis (Qutech, Delft University of Technology)**

**Authors:** Kostas Vilkelis, Lin Wang, Anton Akhmerov

**Preprint:** arXiv:2012.08552

Recent measurements of the out-of-plane magnetoresistance of delafossites (PdCoO\(_2\) and PtCoO\(_2\)) observed oscillations which closely resemble the Aharanov-Bohm effect. We develop a semiclassical theory of these oscillations and show that they are a consequence of the quasi-2D dispersion of delafossites. We observe that the Lorentz force created by an in-plane magnetic field makes the out-of-plane motion of electrons oscillatory, similarly to Bloch oscillations. Analysis of the visibility of these Bloch-Lorentz oscillations reveals the mean-free path to be \(l \approx 4.4 \mu m\) in comparison to the literature in-plane mean free path of \(20 \mu m\). The mean-free path is reduced as a consequence of the out-of-plane relaxation and sample wall scattering. Our theory offers a way to design an experimental geometry that is better suited for probing the phenomenon and to investigate the out-of-plane dynamics of ballistic quasi-two-dimensional materials.

### Floquet Gauge Pump

**By Abhishek Kumar (Indiana University Bloomington)**

**Authors:** Abhishek Kumar, Gerardo Ortiz, Philip Richerme, Babak Seradjeh

**Preprint:** arXiv:2012.09677

We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional XY model with periodically driven couplings and transverse field. In the high frequency limit, we obtain the Floquet Hamiltonian consisting of the static XY and dynamically generated Dzyaloshinsky-Moriya interaction (DMI) terms. The dynamically generated magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. As these phases are cycled, it reveals the ground state degeneracies that distinguish the ordered and disordered phases. We discuss experimental requirements needed to realize the Floquet gauge pump in a synthetic quantum spin system of interacting trapped ions.

### Electronic properties of InAs/EuS/Al hybrid nanowires

**By Chun-Xiao Liu (Delft University of Technology, the Netherlands)**

**Authors:** Chun-Xiao Liu, Sergej Schuwalow, Yu Liu, Kostas Vilkelis, A. L. R. Manesco, P. Krogstrup, Michael Wimmer

**Preprint:** arXiv:2011.06567

We study the electronic properties of InAs/EuS/Al heterostructures as explored in a recent experiment [S. Vaitiekenas \emph{et al.}, Nat. Phys. (2020)], combining both spectroscopic results and microscopic device simulations. In particular, we use angle-resolved photoemission spectroscopy to investigate the band bending at the InAs/EuS interface. The resulting band offset value serves as an essential input to subsequent microscopic device simulations, allowing us to map the electronic wave function distribution. We conclude that the magnetic proximity effects at the Al/EuS as well as the InAs/EuS interfaces are both essential to achieve topological superconductivity at zero applied magnetic field. Mapping the topological phase diagram as a function of gate voltages and proximity-induced exchange couplings, we show that the ferromagnetic hybrid nanowire with overlapping Al and EuS layers can become a topological superconductor within realistic parameter regimes. Our work highlights the need for a combined experimental and theoretical effort for faithful device simulation.

### Strain-engineering the topological type-II Dirac semimetal NiTe2

**By Antonio Manesco (University of São Paulo)**

**Authors:** Pedro P. Ferreira, Antonio L. R. Manesco, Thiago T. Dorini, Lucas E. Correa, Gabrielle Weber, Antonio J. S. Machado, Luiz T. F. Eleno

**Preprint:** arXiv:2006.14071

In this work, the electronic and elastic properties of the type-II Dirac semimetal NiTe\(_2\), in equilibrium and under strain, were systematically studied within the scope of density functional theory (DFT) and effective models. We have demonstrated that strain-engineering is an effective route for manipulating its electronic and topological properties. We have shown that compressive and tensile deformations control the Dirac node momentum and their energy relative to the Fermi level. Moreover, it is possible to lower or increase the overlap between the low-energy wave functions and suppress trivial bands, opening the way for superconductivity, Liftshtz transitions, and a hybrid type-I and type-II Dirac semimetallic phase. Furthermore, we provided a minimal effective model for the Dirac cone and derive the mentioned strain effects using lattice regularization, providing an inexpensive way for further theoretical investigations and easy comparison with experiments. We also proposed statically controlling the electronic-structure with the intercalation of alkali-element species into the van der Waals gap, resulting in a similar physical response to the one obtained by strain-engineering.

### Many-body Majorana-like zero modes without gauge symmetry breaking

**By Vasilii Vadimov (QCD Labs, Department of Applied Physics, Aalto University)**

**Authors:** V. Vadimov, T. Hyart, J. L. Lado, M. Möttönen, T. Ala-Nissila

**Preprint:** arXiv:2011.06552

Topological superconductors represent one of the key hosts of Majorana-based topological quantum computing. Typical scenarios for one-dimensional topological superconductivity assume a broken gauge symmetry associated to a superconducting state. However, no interacting one-dimensional many-body system is known to spontaneously break gauge symmetries. Here, we show that zero modes emerge in a many-body system without gauge symmetry breaking and in the absence of superconducting order. In particular, we demonstrate that Majorana zero modes of the symmetry-broken superconducting state are continuously connected to these zero-mode excitations, demonstrating that zero-bias anomalies may emerge in the absence of gauge symmetry breaking. We demonstrate that these many-body zero modes share the robustness features of the Majorana zero modes of symmetry-broken topological superconductors. We introduce a bosonization formalism to analyze these excitations and show that a ground state analogous to a topological superconducting state can be analytically found in a certain limit. Our results demonstrate that robust Majorana-like zero modes may appear in a many-body systems without gauge symmetry breaking, thus introducing a family of protected excitations with no single-particle analogs.

### Statistical Floquet prethermalization from kicked rotors to the Bose-Hubbard model

**By Dalla Torre Emanuele (Bar-Ilan University)**

**Authors:** Emanuele G. Dalla Torre

**Preprint:** arXiv:2005.07207

The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large frequencies. In particular, for quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we develop a semiclassical description of Floquet prethermal states and link the suppressed heating rate to the low probability of finding many particles on a single site. We derive an analytic expression for the exponential suppression of heating valid at strong interactions and large temperatures, which matches the exact numerical solution of the model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

### Topological phonons in oxide perovskites controlled by light

**By Bo Peng (Cavendish Laboratory, University of Cambridge)**

**Authors:** Bo Peng, Yuchen Hu, Shuichi Murakami, Tiantian Zhang, Bartomeu Monserrat

**Preprint:** arXiv:10.17863/CAM.57482

Perovskite oxides exhibit a rich variety of structural phases hosting different physical phenomena that generate multiple technological applications. We find that topological phonons – nodal rings, nodal lines, and Weyl points – are ubiquitous in oxide perovskites in terms of structures (tetragonal, orthorhombic, and rhombohedral), compounds (BaTiO3, PbTiO3, and SrTiO3), and external conditions (photoexcitation, strain, and temperature). In particular, in the tetragonal phase of these compounds all types of topological phonons can simultaneously emerge when stabilized by photoexcitation, whereas the tetragonal phase stabilized by thermal fluctuations only hosts a more limited set of topological phonon states. In addition, we find that the photoexcited carrier concentration can be used to tune the topological phonon states and induce topological transitions even without associated structural phase changes. Overall, we propose oxide perovskites as a versatile platform in which to study topological phonons and their manipulation with light.

### Long-range ballistic transport of Brown-Zak fermions in graphene superlattices

**By Julien Barrier (The University of Manchester, U.K.)**

**Authors:** Julien Barrier, Piranavan Kumaravadivel, Roshan Krishna-Kumar, L. A. Ponomarenko, Na Xin, Matthew Holwill, Ciaran Mullan, Minsoo Kim, R. V. Gorbachev, M. D. Thompson, J. R. Prance, T. Taniguchi, K. Watanabe, I. V. Grigorieva, K. S. Novoselov, A. Mishchenko, V. I. Fal'ko, A. K. Geim, A. I. Berdyugin

**Preprint:** arXiv:2006.15040

In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational (\(p/q\)) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 10\(^6\) cm\(^2\)V\(^{-1}\)s\(^{-1}\) and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are \(4q\) times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1K. We also found negative bend resistance at \(1/q\) fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field.

### Conductance asymmetries in mesoscopic superconducting devices due to finite bias

**By André Melo (Kavli Institute of Nanoscience, Delft University of Technology)**

**Authors:** André Melo, Chun-Xiao Liu, Piotr Rożek, Tómas Örn Rosdahl, Michael Wimmer

**Preprint:** arXiv:2008.01734

Tunneling conductance spectroscopy in normal metal-superconductor junctions is an important tool for probing Andreev bound states in mesoscopic superconducting devices, such as Majorana nanowires. In an ideal superconducting device, the subgap conductance obeys specific symmetry relations, due to particle-hole symmetry and unitarity of the scattering matrix. However, experimental data often exhibits deviations from these symmetries or even their explicit breakdown. In this work, we identify a mechanism that leads to conductance asymmetries without quasiparticle poisoning. In particular, we investigate the effects of finite bias and include the voltage dependence in the tunnel barrier transparency, finding significant conductance asymmetries for realistic device parameters. It is important to identify the physical origin of conductance asymmetries: in contrast to other possible mechanisms such as quasiparticle poisoning, finite-bias effects are not detrimental to the performance of a topological qubit. To that end we identify features that can be used to experimentally determine whether finite-bias effects are the source of conductance asymmetries.

### Topological Band Structures in the Offset-Parameter-Dependence of Small Josephson Circuits

**By Valla Fatemi (Yale University)**

**Authors:** Valla Fatemi, Anton R. Akhmerov, Landry Bretheau

**Preprint:** arXiv:2008.13758

We introduce Weyl Josephson circuits: small Josephson junction circuits that simulate Weyl band structures. We first formulate a general approach to design circuits that are analogous to Bloch Hamiltonians of a desired dimensionality and symmetry class. We then construct and analyze a six-junction device that produces a 3D Weyl Hamiltonian with broken inversion symmetry and in which topological phase transitions can be triggered *in situ*. We argue that currently available superconducting circuit technology allows experiments that probe topological properties inaccessible in condensed matter systems.

### Landau Quasiparticles in Weak Power-Law Liquids

**By Joshuah T. Heath (Boston College)**

**Authors:** Joshuah T. Heath

**Preprint:** arXiv:2001.08230

The failure of Landau-Fermi liquid theory is often considered a telltale sign of universal, scale-invariant behavior in the emergent field theory of interacting fermions. Nevertheless, there exist borderline cases where weak scale invariance coupled with particle-hole asymmetry can coexist with the Landau quasiparticle paradigm. In this letter, I show explicitly that a Landau-Fermi liquid can exist for weak power-law scaling of the retarded Green's function. Such an exotic variant of the traditional Fermi liquid, although exhibiting a finite quasiparticle weight and large quasiparticle lifetime, is shown to always be incompatible with Luttinger's theorem for any non-trivial scaling. This result yields evidence for a Fermi liquid-like ground state in the high-field, underdoped pseudogap phase of the high-temperature cuprate superconductors.

### Using skyrmionic racetracks for unconventional computing

**By Hamed Vakili (Dept. of Physics University of Virginia)**

**Authors:** Hamed Vakili, Mohammad Nazmus Sakib, Samiran Ganguly, Mircea Stan, Matthew W. Daniels, Advait Madhavan, Mark D. Stiles, Avik W. Ghosh

**Preprint:** arXiv:2005.10704

Skyrmions are topological excitations in thin magnetic films with broken spatial symmetry, and can be driven at high speeds along magnetic racetracks using modest currents in heavy metal underlayers. However, they suffer strong Magnus forces arising from their vorticity. Eliminating these Magnus forces requires precise tuning of parameters that are hard to execute during fabrication. We show how Heusler ferrimagnetic racetracks can achieve high speeds and low damping. Instead of eliminating Magnus forces, we show how designing a spatially varying magnetic parameter, such as a graded PtxW1-x alloy, creates a moving skyrmion that keeps evolving into a growing hybrid between Bloch and Neel until it reaches an automatic compensation line where it self-converges into a racetrack. We can further tune the compensation line using a combination of static and gate-controlled dynamic magnetic anisotropy. Finally, we describe how the position of skyrmions along racetracks can be used as a native memory for temporal race logic that can be used for solving large graph theoretical problems.

### Correlations in the elastic Landau level of spontaneously buckled graphene

**By Antonio Manesco (University of São Paulo)**

**Authors:** Antonio L. R. Manesco, Jose L. Lado, Eduardo V. S. Ribeiro, Gabrielle Weber, Durval Rodrigues Jr

**Preprint:** arXiv:2003.05163

Electronic correlations stemming from nearly flat bands in van der Waals materials have demonstrated to be a powerful playground to engineer artificial quantum matter, including superconductors, correlated insulators and topological matter. This phenomenology has been experimentally observed in a variety of twisted van der Waals materials, such as graphene and dichalcogenide multilayers. Here we show that spontaneously buckled graphene can yield a correlated state, emerging from an elastic pseudo Landau level. Our results build on top of recent experimental findings reporting that, when placed on top of hBN or NbSe\(_2\) substrates, wrinkled graphene sheets relax forming a periodic, long-range buckling pattern. The low-energy physics can be accurately described by electrons in the presence of a pseudo-axial gauge field, leading to the formation of sublattice-polarized Landau levels. Moreover, we verify that the high density of states at the zeroth Landau level leads to the formation of a periodically modulated ferrimagnetic groundstate, which can be controlled by the application of external electric fields. Our results indicate that periodically strained graphene is a versatile platform to explore emergent electronic states arising from correlated elastic Landau levels.